Orthogonal jumps of wavefunction in white-noise potentials

Abstract

We investigate the evolution of the quantum state for a free particle placed into a random external potential of white-noise type. The master equation for the density matrix is derived by means of path integral method. We propose an equivalent stochastic process where the wavefunction satisfies a nonlinear Schr\"odinger equation except for random moments at which it shows orthogonal jumps. The relation of our work to the usual theory of quantum noise and damping is briefly discussed.